Question

Page < 2 > of 2 0 - ZOOM + Additional Problem #2: CHANGING INTEREST RATE PROBLEM Trans-Star, a spin-off company of MOPAR, supplies major automobile transmission components to auto manufacturers worldwide and is Mopar's largest supplier. A Trans-Star Engineer has been tasked with evaluating bids for new-generation CNC machinery to be directly linked to the automated manufacturing of high-precision transmission band components. The following are three interest rates that are included in the Vendor bids. Trans-Star will make payments on a semiannual basis only. The engineer is confused about the effective interest rates-what they are annually and over the payment period of 6-months. Answer the following questions: Bid #1: 8.25% per year, compounded monthly Bid #2: 7.60% per year, compounded quarterly Bid #3: 2.25% per quarter, compounded quarterly a.) Calculate the effective semiannual interest rate for ALL three bids. b.) Calculate the effective annual interest rate for ALL three bids.

Answer 1

a)

Bid 1

Monthly nominal interest rate=i=8.25%/12=0.006875

Number of compounding per half year=c=6

Effective semi annual interest rate=(1+i)^c-1=(1+0.006875)^6-1=4.1966%

Bid 2

Quarterly nominal interest rate=i=7.60%/4=0.019

Number of compounding per half year=c=2

Effective semi annual interest rate=(1+i)^c-1=(1+0.019)^2-1=3.8361%

Bid 3

Quarterly nominal interest rate=i=0.0225

Number of compounding per half year=c=2

Effective semi annual interest rate=(1+i)^c-1=(1+0.0225)^2-1=4.5506%

b)

Bid 1

Monthly nominal interest rate=i=8.25%/12=0.006875

Number of compounding per year=c=12

Effective annual interest rate=(1+i)^c-1=(1+0.006875)^12-1=8.5692%

Bid 2

Quarterly nominal interest rate=i=7.60%/4=0.019

Number of compounding per year=c=4

Effective annual interest rate=(1+i)^c-1=(1+0.019)^4-1=7.8194%

Bid 3

Quarterly nominal interest rate=i=0.0225

Number of compounding per year=c=4

Effective semi annual interest rate=(1+i)^c-1=(1+0.0225)^4-1=9.3083%